By default, if you are a member of a Google Group or Collaborative Inbox, you will receive a copy of every email that is sent to the group.
You can change this setting so that you don't receive emails in your own Gmail account, or you can choose to receive an abridged summary each day, or a digest of each 25 messages.
To change group notifications:
In the main Google Groups screen, position the mouse over the group you wish to set the option for
Click on the Subscription drop-down
Choose how you wish to receive emails e.g. None
The following options are available:
Each email—Messages sent individually as they’re posted to the group
Digest—Up to 25 complete messages combined into single emails and sent daily
Abridged—Summaries of up to 150 messages combined into single emails and sent daily
No email—Messages from the group are not sent